{
  "id": "math/0403263",
  "version": "v3",
  "published": "2004-03-16T13:57:38.000Z",
  "updated": "2017-08-22T01:27:25.000Z",
  "title": "Optimality and uniqueness of the Leech lattice among lattices",
  "authors": [
    "Henry Cohn",
    "Abhinav Kumar"
  ],
  "comment": "39 pages",
  "journal": "Annals of Mathematics 170 (2009), 1003-1050",
  "doi": "10.4007/annals.2009.170.1003",
  "categories": [
    "math.MG"
  ],
  "abstract": "We prove that the Leech lattice is the unique densest lattice in R^24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in R^24 can exceed the Leech lattice's density by a factor of more than 1+1.65*10^(-30), and we give a new proof that E_8 is the unique densest lattice in R^8.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-09-30T21:20:51.000Z",
      "comment": "39 pages, to appear in Annals of Mathematics"
    },
    {
      "version": "v3",
      "updated": "2017-08-22T01:27:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unique densest lattice",
      "optimality",
      "uniqueness",
      "leech lattices density",
      "computer verification"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3263C"
    }
  }
}